Nonlinear model-based control of the Czochralski process II: Reconstruction of crystal radius and growth rate from the weighing signal

In this contribution a nonlinear observer for reconstruction of not directly measured quantities in Czochralski and liquid encapsulated Czochralski crystal growth is derived. The observer can be used in control systems which require knowledge of the crystal radius, of the crystal slope angle, and of the crystal growth rate. Using a nonlinear lumped parameter model these quantities are reconstructed from the weight gain signal which is usually available in growth plants. In contrast to existing solutions found in the literature the nonlinear observer can be used throughout the whole process, especially when growing the conical parts in which the dynamics of the process is changing heavily. The capability of the observer as well as thorough investigations regarding its robustness are illustrated using simulations and experimental results.